Question: Simplify to lowest terms. $\dfrac{30}{12}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 30 and 12? $30 = 2\cdot3\cdot5$ $12 = 2\cdot2\cdot3$ $\mbox{GCD}(30, 12) = 2\cdot3 = 6$ $\dfrac{30}{12} = \dfrac{5 \cdot 6}{ 2\cdot 6}$ $\hphantom{\dfrac{30}{12}} = \dfrac{5}{2} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{30}{12}} = \dfrac{5}{2} \cdot 1$ $\hphantom{\dfrac{30}{12}} = \dfrac{5}{2}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{30}{12}= \dfrac{2\cdot15}{2\cdot6}= \dfrac{2\cdot 3\cdot5}{2\cdot 3\cdot2}= \dfrac{5}{2}$